There are 2 vehicles. Vehicle 1 a ford taurus at 3400 pounds is traveling 50mph headed east. Vehicle 2 is a dodge ram truck at 6400. The truck hits the car head on and the car is pushed back 35 feet from point of impact. The truck is 90 feet from point of impact. How fast was the truck going just before hitting the taurus?
To determine the speed of the truck just before hitting the Taurus, we can use the principle of conservation of momentum.
First, let's calculate the initial momentum of the system (combined momentum of both vehicles) before the collision. Momentum is given by the equation:
Momentum = Mass x Velocity
For Vehicle 1 (Taurus), the mass is 3400 pounds. We need to convert it to a standard unit like kilograms for the calculation. 1 pound is approximately 0.454 kilograms, so the mass of Vehicle 1 is 3400 x 0.454 = 1546.36 kg.
For Vehicle 2 (Ram truck), the mass is 6400 pounds. Converting it to kilograms, we get 6400 x 0.454 = 2909.6 kg.
Now, we need to find the velocity of the Taurus. We are given that it traveled 35 feet back from the point of impact. We'll need to convert this into meters for the calculation. 1 foot is approximately 0.3048 meters, so the distance traveled by the Taurus is 35 x 0.3048 = 10.668 meters.
The velocity of the Taurus is the distance traveled divided by the time taken. Since the time is not given, we cannot directly calculate the velocity of the Taurus. Therefore, we'll need to make some assumptions or use additional information to determine the time.
If we assume that the collision between the two vehicles is instant (negligible time of impact), then we can calculate the initial momentum just before the collision and set it equal to the final momentum just after the collision. Mathematically, the equation would be:
Initial Momentum of Vehicle 1 + Initial Momentum of Vehicle 2 = Final Momentum of Vehicle 1 + Final Momentum of Vehicle 2
m1 * v1 + m2 * v2 = (m1 + m2) * vf
Where:
m1 = mass of Vehicle 1
v1 = velocity of Vehicle 1
m2 = mass of Vehicle 2
v2 = velocity of Vehicle 2
vf = final velocity after the collision
We know the masses of both vehicles and the velocity of Vehicle 1 but need to find the final velocity (vf).
After the collision, the Taurus is pushed back 35 feet, which means it slows down. Therefore, vf (final velocity) would be negative since the Taurus is traveling in the opposite direction.
Now, we can plug in the known values:
m1 = 1546.36 kg (mass of Taurus)
v1 = velocity of Taurus (unknown)
m2 = 2909.6 kg (mass of Ram truck)
v2 = velocity of Ram truck (unknown)
vf = -v1 (Taurus' final velocity is negative and has the same magnitude as its initial velocity)
The equation becomes:
1546.36 kg * v1 + 2909.6 kg * v2 = (1546.36 kg + 2909.6 kg) * (-v1)
Simplifying the equation:
1546.36 kg * v1 + 2909.6 kg * v2 = -4455.96 kg * v1
Now, we need to use the distance information provided to establish a relationship between the velocities of the two vehicles.
The distance traveled by the Ram truck is given as 90 feet. Converting it into meters, we get 90 * 0.3048 = 27.432 meters.
Since the truck traveled further than the car, we'll assume that the time it took for both vehicles to reach the point of impact is the same (uniform motion assumption).
Therefore, the time taken by both vehicles is the same, which means the time it took for the Ram truck to travel 27.432 meters is the same as the time it took for the Taurus to travel 10.668 meters. This relationship can be written mathematically as:
v2 / v1 = distance2 / distance1
v2 / v1 = 27.432 / 10.668
Now, we can substitute this relationship into the previous equation:
1546.36 kg * v1 + 2909.6 kg * (27.432 / 10.668) * v1 = -4455.96 kg * v1
Simplifying further:
1546.36 kg * v1 + 2909.6 kg * 2.5706 * v1 = -4455.96 kg * v1
1546.36 kg * v1 + 7477.298 kg * v1 = -4455.96 kg * v1
9023.658 kg * v1 = -4455.96 kg * v1
Since both sides of the equation are equal, we can cancel the v1 term:
9023.658 kg = -4455.96 kg
This equation cannot be true since the left side is positive and the right side is negative. Therefore, there must be some error or assumption made in the problem statement. Please recheck the given information or provide any additional details necessary to solve the problem accurately.